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Sarah C.

two triangles are congruentif and only if...?

their vertices can be matched up so that their corresponding parts (angles and sides) of the triangles are congruent.

SSS Postulate

If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.

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SAS Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

A line and a plane are perpendicular if and only if...?

they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.

A Way to Prove Two Segments or Two Angles Congruent

1) Identify two ___?___ in which the two segments or __?__ are ___?___ parts.

2) Prove that the ___?___ are congruent.

3) State that the two parts are __?__, supporting the statement with the reason: ____?____

1) triangles, angles, corresponding

2) triangles

3) Correspondin parts of congruent triangles are congruent

congruent sides of a triangle are called __?__.

the third side of the triangle is called the __?__.

the angle opposite the base is known as the __?__ __?__ of the isosceles triangle.

1) legs

2) base

3) vertex angle

the Isosceles Triangle Theorem

If two sides of a triangle are congruent then the angles opposite those sides are congruent

Corollary 1 of Isosceles Theorem

An equilateral triangle is also equiangular.

Corollary 2 of Isosceles Theorem

An equilateral triangle has three 60 degree angles.

Corollary 3 of Isosceles Theorem

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

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If two __?__ of a triangle are __?__, then the three __?__ opposite those angles are __?__ (Theorem 3-2)

angles, congruent, sides, congruent

Corollary 1 (of Theorem 3-2)

An equiangular triangle is also equilateral

AAS Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

HL Theorem

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

hypotenuse

in a right triangle the side opposite the right angle (the other two legs are called legs).

median of a triangle

a segment from a vertex to the midpoint of the opposite side.

altitude of a triangle

the perpendicular segment from a vertex to the line that contains the opposite side.

always, sometimes or never?

1) the medians of a triangle are __?__ inside the triangle.

2) the altitudes of a triangle are __?__ inside the triangles.

1) always

2) sometimes

perpendicular bisector of a segment

a line (or ray or segment) that is perpendicular to the segment at its midpoint.

distance from a point to a line (or plane)

the length of the perpendicular segment from the point to the line (or plane).

If a point lies on the __?__ bisector of a segment, then the point is __?__ from the __?__ of the segment (Theorem 3--5)

perpendicular, equidistant, endpoints

I a point is __?__ from the endpoints of a __?__, the the point lies on the perpendicular __?__ of the segment. (Theorem 3--6)

equidistant, segment, bisector

If a point lies on the __?__ of an __?__, the the point is equidistant from the __?__ of the angle. (Theorem 3--7)

bisector, angle, sides

If a point is __?__ from the sides of an __?__, then the point lies on the __?__ of an angle. (Theorem 3--8)

equidistant, angle, bisector

Deductive Reasoning

1) Conclusion based on accepted statements (?,?,?,?,?and ?)

2) Conclusion __?__ be true if the hypothese are true.

1) definitions, postulates, previous theorems, corollaries, and given information.

2) must

Inductive Reasoning

1) Conclusion based on?

2) Conclusion os __?__ true , but not necessarily true.

1) several past observations.

2) probably

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